Therefore, I conclude, he stopped in London for the night, sleeping at an hotel, without luggage, and paying for his room in advance.

It is frequently done, and if he arrived late, very little notice would be taken of him.

Big hotels about the Strand, I am told, have always a dozen such casual bachelor guests every evening." "And then ?" "And then, this morning, he would buy a new bicycle--a different make from his own, at the nearest shop; would rig himself out, at some ready-made tailor's, with a fresh tourist suit--probably an ostentatiously tweedy bicycling suit; and, with that in his luggage-carrier, would make straight on his machine for the country.
He could change in some copse, and bury his own clothes, avoiding the blunders he has seen in others.

Perhaps he might ride for the first twenty or thirty miles out of London to some minor side-station, and then go on by train towards his destination, quitting the rail again at some unimportant point where the main west road crosses the Great Western or the South-Western line." "Great Western or South-Western?
Why those two in particular?
Then, you have settled in your own mind which direction he has taken ?" "Pretty well.

I judge by analogy.